Finite mixtures of normal distributions in the study of the error in altimetry

The modelling of the altimetric error is proposed by means of the mixture of normal distributions. This alternative allows to avoid the problems of lack of normality of the altimetric error and that have been indicated numerous times. The conceptual bases of the mixture of distributions are presented and its application is demonstrated with an applied example. In the example, the altimetric errors existing between a DEM with 5 × 5 m resolution and another DEM with 2 × 2 m resolution are modelled, which is considered as a reference. The application demonstrates the feasibility and power of analysis of the proposal made.

Clustering repeated ordinal data: Model based approaches using finite mixtures

<p>Model based approaches to cluster continuous and cross-sectional data are abundant and well established. In contrast to that, equivalent approaches for repeated ordinal data are less common and an active area of research. In this dissertation, we propose several models to cluster repeated ordinal data using finite mixtures. In doing so, we explore several ways of incorporating the correlation due to the repeated measurements while taking into account the ordinal nature of the data. In particular, we extend the Proportional Odds model to incorporate latent random effects and latent transitional terms. These two ways of incorporating the correlation are also known as parameter and data dependent models in the time-series literature. In contrast to most of the existing literature, our aim is classification and not parameter estimation. This is, to provide flexible and parsimonious ways to estimate latent populations and classification probabilities for repeated ordinal data. We estimate the models using Frequentist (Expectation-Maximization algorithm) and Bayesian (Markov Chain Monte Carlo) inference methods and compare advantages and disadvantages of both approaches with simulated and real datasets. In order to compare models, we use several information criteria: AIC, BIC, DIC and WAIC, as well as a Bayesian Non-Parametric approach (Dirichlet Process Mixtures). With regards to the applications, we illustrate the models using self-reported health status in Australia (poor to excellent), life satisfaction in New Zealand (completely agree to completely disagree) and agreement with a reference genome of infant gut bacteria (equal, segregating and variant) from baby stool samples.</p>

Clustering repeated ordinal data: Model based approaches using finite mixtures

<p>Model based approaches to cluster continuous and cross-sectional data are abundant and well established. In contrast to that, equivalent approaches for repeated ordinal data are less common and an active area of research. In this dissertation, we propose several models to cluster repeated ordinal data using finite mixtures. In doing so, we explore several ways of incorporating the correlation due to the repeated measurements while taking into account the ordinal nature of the data. In particular, we extend the Proportional Odds model to incorporate latent random effects and latent transitional terms. These two ways of incorporating the correlation are also known as parameter and data dependent models in the time-series literature. In contrast to most of the existing literature, our aim is classification and not parameter estimation. This is, to provide flexible and parsimonious ways to estimate latent populations and classification probabilities for repeated ordinal data. We estimate the models using Frequentist (Expectation-Maximization algorithm) and Bayesian (Markov Chain Monte Carlo) inference methods and compare advantages and disadvantages of both approaches with simulated and real datasets. In order to compare models, we use several information criteria: AIC, BIC, DIC and WAIC, as well as a Bayesian Non-Parametric approach (Dirichlet Process Mixtures). With regards to the applications, we illustrate the models using self-reported health status in Australia (poor to excellent), life satisfaction in New Zealand (completely agree to completely disagree) and agreement with a reference genome of infant gut bacteria (equal, segregating and variant) from baby stool samples.</p>

Matrix Normal Cluster-Weighted Models

Finite mixtures of regressions with fixed covariates are a commonly used model-based clustering methodology to deal with regression data. However, they assume assignment independence, i.e., the allocation of data points to the clusters is made independently of the distribution of the covariates. To take into account the latter aspect, finite mixtures of regressions with random covariates, also known as cluster-weighted models (CWMs), have been proposed in the univariate and multivariate literature. In this paper, the CWM is extended to matrix data, e.g., those data where a set of variables are simultaneously observed at different time points or locations. Specifically, the cluster-specific marginal distribution of the covariates and the cluster-specific conditional distribution of the responses given the covariates are assumed to be matrix normal. Maximum likelihood parameter estimates are derived using an expectation-conditional maximization algorithm. Parameter recovery, classification assessment, and the capability of the Bayesian information criterion to detect the underlying groups are investigated using simulated data. Finally, two real data applications concerning educational indicators and the Italian non-life insurance market are presented.